A084827 Maximum number of spheres of volume one that can be packed in a sphere of volume n.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 6, 6, 6, 7, 8, 8, 9, 9, 10, 10, 12, 12, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 23, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 34, 35, 36, 36, 38, 38, 38, 38, 39, 39, 40, 40, 42, 42, 42, 43, 43, 44

Offset

1,8

Comments

Higher terms of the sequence are only conjectures derived from numerical results. The first 12 arrangements are identical with the solutions of the Tammes problem (see A080865).

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..132

Hugo Pfoertner, Densest packings of n equal spheres in a sphere of radius 1 (Table of largest possible radii)

Hugo Pfoertner, Numerical results for best packing of spheres in sphere.

Eric Weisstein's World of Mathematics, World of Mathematics: Sphere Packing.

Example

a(10)=2 because a sphere of volume 10 is slightly too small to cover 3 mutually touching spheres of volume 1. a(27)=13 because the arrangement of 12 spheres plus one central sphere needs exactly a sphere with R=3*r to be contained.

Crossrefs

Cf. A084828, A084829, A084824, A080865.

Sequence in context: A369573 A117953 A128331 * A251631 A029076 A259774

Adjacent sequences: A084824 A084825 A084826 * A084828 A084829 A084830

Keyword

hard,nonn

Author

Hugo Pfoertner, Jun 09 2003

Extensions

More terms from Hugo Pfoertner, May 09 2005

Status

approved